What We Modeled
The main focus of our team was determining the optimal growth conditions of Rhizobium tropici for the fact sheet as well as for our own experiments. After noticing that we struggled to create nodules in the roots of our plants, we were curious whether or not our soil growth conditions were optimal for the Rhizobium. To figure out how we could improve soil conditions for easier nodulation, we measured the growth rate of the rhizobium in many different temperatures and media.
How We Modeled our Data
These models were all created in Google Colab, a Python-based development environment, using optical density measurements. They are based on the assumption that bacterial growth follows a logisitc/sigmoidal curve, which is where the density of the sample increases exponentially until a certain point at which point the growth slows down and levels out. The general equation for a sigmoidal curve is
where a controls how steeply the function grows, b is the time at which the growth switches from exponential to logarithmic, and c is the maximum value. Taking the derivative of this function and evaluating at x = b, which is where the bacteria are growing the most quickly, yields a*c/4. This is the maximum generation time, and the doubling time can be calculated by dividing the natural logarithm of 2 by this time. All of the graphs below where generated with these assumptions and this model.
Temperature
Our first thought was that the growth temperature of the soil was suboptimal. They were being grown at room temperature since we did not have an incubator large enough to hold all of the samples. In order to test this hypothesis, we grew samples of Rhizobium at room temperature (approximately 20°C) and 29°C. The models generated to fit these measurements, which were grown in Yeast Mannitol Low Calcium media, along with their maximum doubling time, are shown below.
Optimal doubling time: 4.48 hours
Optimal doubling time: 4.88 hours
These two models indicate that temperature may not be the main factor responsible for the lack of nodulation. The slight difference in doubling time can likely be attributed to sampling error and random variation, although we would need to repeat these results and do statistical tests to show that the difference is not meaningful. However, our experimental findings match this conclusion, since even when some of the plants were transferred to an incubator at a higher temperature, the presence of nodules was not increased. Over the course of the weeks they were allowed to grow, this small of a difference should not have had that much of an impact, but since the bacteria do grow more slowly at lower temperatures, if we were to repeat the experiment again and we could not use a greenhouse to incubate at a higher temperature, this might mean that we should wait longer to check for nodule formation.
Media
Our second thought was that the conditions of the soil were not conducive to the growth of our rhizobium. As explained in the Engineering page, we selected Yeast Mannitol Low Calcium medium because it seemed to encourage the most growth of our rhizobacteria. However, we also saw that a previous iGEM team that worked with R. tropici, Yale 2016, used Tryptic Soy Broth instead. We were curious if the rhizobacteria might grow better in this media, which would give us information on how we could encourage more nodule formation. To test this, we compared the growth rates of rhizobacteria grown in our Yeast Mannitol Low Calcium medium against those of rhizobacteria grown in Tryptic Soy Broth at 29°C. The data points and fitted models can be found below:
Optimal doubling time: 4.88 hours
Optimal doubling time: 1.75 hours
This difference is much more significant than that caused by temperature. These experiments tell us that we may be able to provide a better growth media for the Rhizobium, and if we were to continue with this project in the future, we would use such acould try adding nutrients like those found in tryptic soy broth to our soil mixture instead of using only African violet soil.